# Hex Vs tet meshing in CFD

1. Sep 23, 2008

### mahaesh

Hi everyone!
Can you explain me Why always hex mesh is preffered instead of tet mesh if hex mesh is possible in perticular geometry? give brief explanation as flux point of view.

2. Sep 23, 2008

### minger

For the stuff that I've done, a hex is sometimes needed if high-order schemes are being used, as a structured mesh is needed.

3. Sep 24, 2008

### PerennialII

Not even trying to provide a complete answer, but would say that hex element types have typically better "accuracy" (with the type and degree of interpolation they possess as well as element shape (aspect ratio, distortion etc.) related issues, if you perform for example error estimation) for solving most PDEs. In addition, structured/mapped/hex meshes typically have better "quality" (could call it distribution, position (and just overall control) of degrees-of-freedom in the model). There is a whole lot more to be said about this if interested or want to read more.

4. Sep 24, 2008

### minger

I would have to disagree with you Perennial, maybe it's mostly semantics, but either way. I would argue that no grid type has better "accuracy" than another type. Tets can give better answers than hex meshes, and vice versa. I will agree that using structured hex meshes give you ability to use high order of accuracy; but that concept is not directly related to the actual accuracy. Using first-order tet elements with localized bunching can give you a better answer in less computation time than hexes. Again though, it's on a case by case basis.

However, in the field of aeroacoustics, I would say that structured hexes are a necessity, when possible. This goes back to the concept of order of accuracy. Order of accuracy is defined as the rate at which the error decreases with decreasing mesh spacing. The error can decrease exponentially though for higher order schemes. For example, when halfing the grid spacing, for a single order scheme, the error decreasing by:

$$\epsilon = (2)^1 = 2$$

Where 2 is the grid density factor, and 1 is the order of the scheme being used. If I were to use a 6th order DRP scheme, I would expect the error to drop by:

$$\epsilon = (2)^6 = 64$$

Now that's not to say that a higher order scheme will always out perform a low order scheme, because that's not the case. In fact, at large grid spacing, one can show that a low order scheme actually provides a better solution with less error. However, if one needs very very high accuracy (as in the case of aeroacoustics), then one can easily see that in order to get the desired accuracy from a first-order scheme, the grid density will need to become ridiculous; whereas there will be a crossing point where the high-order scheme becomes less computationally heavy.

IMHO, CFD is still very much a black or grey art/practice, where the user really needs to understand much of what's going on behind the scenes in order to determine how much to believe the answer.

5. Sep 24, 2008

### mahaesh

but again I have some doubt In CFD It is always criteria that your grid elements(hex/tet) should be along flow direction then I think that Hex are always better than tet mesh.

6. Sep 24, 2008

### PerennialII

I'd think you're not really disagreeing , since the "accuracy" especially as a loose definition like being used in this discussion is a property dependent on so many things. Grid type itself doesn't lead a solution being better than some other, but what I'm arguing is that "typically" if we don't dig deeper then a hex design is "as a rule somewhat preferable" (such rule may not have much generality however for a particular appl, that "grey area" of things). In many cases a tet one will do a better job and in many cases a hex one, there are no general rules in this sense since "accuracy" is not a property directly related to grid type. Need to fix more things to get there. As you mention, it's often most interesting how a better solution can be attained by purposely decreasing the "accuracy" of certain features in your mesh/model.

7. Sep 24, 2008

### minger

Definitely, that's kinda why I said it's mostly semantics.